Forming operations for many applications include bending a sheet of material through a large bend angle, such as 20° to 180°, to produce a permanently deformed or bent band. An example of this process is “hemming”, in which the edge of a sheet is folded over itself by bending it through an angle of 180°. Hemming is used, for example, in automobile assembly, to join inner and outer closure panels, such as in car doors or deck lids, for functional, safety or aesthetic considerations.
To evaluate the mechanical strength of the sheet after bending, and control the introduction of defects during the forming process, it is important to obtain and consider the strain distribution in the deformed region. In hemming, for example, undesirable recoil and surface warp may be introduced by large strains.
Strain measurement in the region of a large bend angle is the focus of ongoing research and development because of the difficulties involved in measuring highly localized and nonlinear deformations. In the case of hemming, for example, the sheet thickness is t˜1 mm and the outer surface of the bent region has a nominal radius of only 2t ˜2 mm. The dimension of the region within which the maximum strain is concentrated is much smaller, of the order of tens of microns. Consequently, the strain measurement method must have a correspondingly high resolution.
Because of localized large plastic strains, the strain measurement of large-angle bending is difficult or complicated using existing methods. Currently, two experimental techniques are commonly used for measuring strain distribution on the deformed region of sheet components: the grid method, and the moiré method with Fourier transforms. A description of the grid method can be found in an article entitled “New Approach to Metal Forming Problems”, by E. G. Thomsen (Trans. ASME, vol. 77, 1955, 515-522), and another article entitled “Determination of the large strains in metal forming”, by R. Sowerby, E. Chu, and J. L. Duncan (J. Strain analysis, 1982, vol. 17(2), 95-101). The moiré method is described in “Application of Moiré Analysis of Strain Using Fourier transform”, by Y. Morimoto, et al. (Opt. Eng., Vol. 27 (8), 1988, 650-656). Both the grid and moiré techniques require analysis of digitized images of surfaces of the deformation region to obtain measurements of the geometry of the deformation process, but they differ significantly in the analytical procedure used to derive strain from displacement.
Generally stated, grid methods divide the area of interest into line or area units and provide values of strain that are averages over each unit. The smaller the grid size, the greater the resolution and accuracy. The strain measured with a grid method is attributed to the geometric center of each area unit and therefore the measurement process is discrete in nature. The main disadvantage of the grid methods when applied to large deformation sheet deformation is that critical strain concentrations caused by steep gradients cannot be captured accurately because of the averaging inherent to the grid discretization. Examples of patterns that can be used with the grid method are shown in FIGS. 11a, 11b and 11c. 
In the moiré method, a pattern consisting of identical unidirectional lines, oriented parallel to the bent line, or a grid consisting of identical squares can be used to measure sheet bending displacements. A moiré pattern is typically generated by the superposition of two gratings: a model grating and master grating (geometric moiré). Since the displacement information is obtained from the master grating pitch for the points of maximum and minimum light intensity of moiré fringes, the smallest strain that can be measured depends in part on the density of the pattern. The accuracy of the measured strain is also dependent on the number of data points analyzed from the captured image of the deformed grating. In principle, Fourier analysis for strain determination considers all points within the deformed grating. The resolution obtained in practice is, however, limited to the number of pixels in a coupled charged device (CCD) camera that is used to take the images and in the operational magnification. An example of a pattern that can be used with the moiré method is shown in FIG. 11b. 
New methods of strain measurement for large angle bending that do not require a grid or a pattern to be imprinted on the surface of strain measurement are, therefore, desirable.